Spectra Of A Class Of Unbounded Operator Matrices

This thesis studies the spectrum,point spectrum,residual spectrum and continuous spectrum of a class of 2×2 operator matrices employing the method of Schur comple-tion. First of all, based on the subdivision of the point spectrum and residual spectrum, we characterize four types of point spectra and two types of residual spectra of the off-diagonal domain operator matrices with at least one invertiblc off-diagonal element. Next, the descriptions of the spectrum, point spectrum, residual spectrum and continuous spec-trum of operator matrices with natural domain are studied. Finally, some examples are presented to illustrate our results.